-r
(~~v
A
REPORT
OF
THE
FACTORS
ACCURACY
submitted
AN
ON
to the
INVESTIGATION
AFFECTING
BUBBLE
OF
THE
METERS
Secretary of the
Faculty
as a partial fulfillment of the requirements
for
the
degree
of
Bachelor
submitted
by
of
Science
g--June 1, 1922.
-
I wish to take this opportunity to
express my thanks to Professor
R. T. Wilson,
who suggested the investigation,
Mr.
G. R. Taylor who offered many
and also to
valuable
suggestions during the course of the investigation.
June 1, 1922
Signed.
Table of Contents
Introduction-------------------Page 1
Types of Flow Meters------------" 1
Factors Involved----------------" 3
Apparatus------------------" 6
Plate 1 ------------------------ " 8
Details of the Investigation--" 9
Plate 2 ------------------------ " 11
3 ----------------------- "12
4 ----------------------- "13
5 ----------------------- "14
6 ------------------------ " 15
7 ----------------------- "17
8------------------------ "18
"t
9------------------------ "20
10 ----------------------- "-21
11 ------------------------- "22
12 ----------------------- "23
Future Work-------------------" 24
25
Conclusions--------------------
"
Data Sheets-+-----------------
"26
130535
A. Introduction
In experimental work of a chemical
nature the reactions of gases play a very important part.
Due to the comparatively large
spaces between the molecules of gases, and due
also to the rapid rates of diffusion, gases
mix both rapidly and completely, the accompanying reactions being frequently the cause of
heat evolution.
The evolution of heat often
passels unnoticed in laboratory experiments but
almost always must be considered in.reactions
that are to be carried on under industrial
conditions.
Complete control of exothermic
reactions is,therefore, an absolute necessity
because of the cumulative effect of heat liberThere are also many other types of gas
ation.
reactions used in laboratory practice which
must be under complete control in order to
As an accurate knowledge of
insure safety.
fact must precede regulation of any kind, so,
before regulating the flow of a gas, its rate
of flow must be known and a flow meter of some
kind must be used.
B. Types of Flow Meters
The flow meters available for the measurement of the flow of fluids, whmle entirely
satisfactory for many things, still leave a great
It can readily be seen that
deal to be desired.
a prime requirement for a meter, to measure gases
in the laboratory, is the ability to measure low
If such a meter
velocities and small volumes.
can be made, that will also have the ability to
withstand corrosion, the advantages to be obtained
Two of the
by its use are greatly increased.
.2
most common and reliable types of instruments are
Wide as is the
Pit~t tubes and Venturi meters.
field of these meters it does not include that of
the measurement of low velocities; in fact the
minimum velocitie-s which such instruments will
measure has been placed by Bentoni at 1.75 cubic
Displacement meters, although
feet per minute.
very accurate, do not give direct readings of
volumes but a reading which must have a correctThis type of meter also has anion applied.
other very serious disadvantage, that is that
it is not of the continuous action type and must
be placed at one or the other ends of the apparAnemometers are expensive, easily corroded,
atus.
Orifices can
and inaccurate at low velocities.
be made in glass and will not be corroded, but
as the small hole necessitated by low velocities
is not only very hard to make, but also requires
very careful calibration, the use of such a meter
Resistance tube
entails certain disadvantages.
meters, which depend on the friction drop in
pressure over a length of pipe, are good instruments for the measurement of small volumes, but
also require careful calibration
The most common type of flow-meter for
laboratory use is the capillary tube meter, a
combination of the orifice and resistance tube
It consists of a tubeabout three
types.
quarters of an inch in diameter, which is connected to the arms of a plain or multiplying
differential guage and having a piece of capillary tubing , passing through a rubber stopper,
placed between the guage, connections in the large
This type of flow meter gives excellent
tube..
results for small volumes but the capillary
frequently becomes plugged and the meter like
many others requires careful calibration.
Calibration of meters for small volumes consists
of passing air through the meter being calibrated
and also through a mechanical meter in series
with it, but as mechanical meters have a large
percentage of error in measuring small volumes,
the percentage error in measurements made by
the calibrated meter will also be high.
A bubble-meter, the possibilities of
which I propose to investigate, will allow the
gas flowing to bubble througha layer of liqutd
which, of course, must be inert with respect to
The volume
the gas flowing through the meter.
of gas passing through the meter will be equal
to the number of bubbles multiplied by a constant.
The determination of this constant for various
conditions of meter operation is the problem of
this investigation.
C. Factors Involved
The factors which will cause variations
in the operation of the bubble-meter and which
therefore must be investigated by passing air
through the meter and noting the volume-number
relations are:
1. The meter liquid.
a. Water.
b. Varied concentrations of
sulphuric acid.
c. Effect of impurities.
I.'
Soap.
2.1
Oil.
4
2.
3.
The exit tip.
a. Size.
b. Type.
The liquid head.
The liquid to be used in the meter must
This requirement
be inert to the gas flowing.
can be practically fullfilled by many different
Water however
liquids, chief of which is water.
does keep many gasets in solution, but as thesaturation point of the meter liquid would be quickly reached, this disadvantage is of slight account.
Water does have another disadvantage, namely, that
it would humidify the air passing through the
Sulphuric acid has many advantages over
meter.
water as a meter liquid chief of which are inactivity towards most gases and low vapor pressure
with the resultant low magnitude of evaporation
Hydrogen sulphide, hydrogen bromide
losses.
and hydrogen iodide will react with sulphuric
acid at the temperatures at which such a meter
would be used, consequently their measurement
with sulphuric acid as a meter liquid is
impossible.
The effect of changing the concentration of the meter liquid will be to change the
specific gravity and also the surface tension.
Of these two factors the second is very important
Another effect of
as will be shown later.
changing the concentration will be to change the
Of course
moisture content of the gas flowing.
by choosing a suitable concentration to be used
the moisture content of the exit gases can be
kept where desired.
5
The size of the exit tUbp is important as
it determines the size of the bubble to ascend
through the liquid and consequently the number per
unit volume of gas.
The effect of changing the
depth of the liquid will be to change the size
of the bubbles and also, for a constant gas
pressure to change the volume of gas to pass
through the meter.
The "Law of Tate" which states that the
weight of a drop, 'W, is proportional to 2frr~
where r is the radius of the dropping tip andY~
is the surface tension of the liquid, has been
proven .approximately true by Harkins 2 .
He has
shown that the weight of a drop is determined
not only by the factors mentioned but also by the
shape of the drop while forming.
This shape
factor is, however, constant for a single dropping tip.
In order to apply the law or a similar one to bubbles the weight term"W"Vould have
to be replaced by the difference in weight of
the bubble and the displaced liquid, which is
to say by the bouyancy of the bubble, the other
factors representing the "Law of Tate" being
unchanged..
As this investigation was not unders
taken for the purpose of determining the weight
or accurate volume. of a bubble, but rather to
study bubbles of constant volume, reference has
been made to the !Law of Tate" and the work of
Harkins only to determitne the factors which will
cause a change in the volume. of a bubble.For
a given set of conditions within the meter the
bubbles are of constant volume and the volume
of gas to be measured is the product of the number
of bubbles and the volume of one bubble.
If the
rate of flow is uniform the fact that some bubbles
6
are disengaged from the end of the tube before
they have attained full growth will not interfere
with the measurement of volume by this method as
the bubbles will still be of constant volume for
any definite velocity.
D. Apparatus
The apparatus used in this investigation is sketched diagrammatically in Plate 1
Air
to which the following letters refer.
ffom the laboratory pipe line was passed through
an Allihn gas wash bottle "A" which contained
the same kind and concentration of liquid as was
Between
in bottle "B", a Bunsen wash bottle.
bottles "A" and "B" was placed a glass tee and
two pinch cocks, one( of the screw type and one
The branch of the
of the spring pinch type.
tee was connected to the first of two similar
By regulating
Bunsen bottles containing water.
the screw clamp "H", the amount of air passing
through bottle "B" could be controlled and the
excess air would be diverefed through bottles
By keeping the ratio of air passing
"C" and "D".through bottles "C" and "D",to that passing
through bottle "B", high, the effects of a varThe backiation of air pressure are minimized.
pressure was kept constant by means of the arrangeA small
ment shown at the bottom of Alate 1.
pan "G" was placed inside the larger pan "F";
in the smaller pan was a glass tube fastened to a
board,, on which graduate "E" was placed, with the
end of the tube level with the top of the pan; as
this pan was always full of water the back;pressure
on bottle "B" was constant and always equal to
atmospheric pressure plus the pressure necessary to
U
7
overcome the friction in the rubber hose leadfrom bottle "B" to pan "G".
The larger pan
served merely to catch the water which continuously overflowed from pan "G".
The volume of
air measured by the graduate, being under less
than atmospheric pressure, should be corrected
but as this correction at its maximum is less
than four percent, and very seldom that, it has
been neglected in many cases, only being applied
for the displacement of water near the top of
the graduate.
U-i
~1~
DETAILS
I
OF
THE
INVESTIGATION.
9
Of the factors which could cause a
variation in the volume of a bubble, the first
investigated was the size and type of tip used.
Tips of different sizes were used in bottle "B",
hereinafter refered to as the meter.
The volume
number relation is shown in Plates 2,3,4 andt5,
from a comparison of which it can be seen that
the inside diameter of the tube is the controilling factor and the outside diameter has little,
if any,effect.
The tube diameters were obtained by the use of micrometers and tapered pins;
the internal diameters were measured by inserting
tapered pins in the tubes and measuring with the
micrometers the largest diameter that would enter
The measurement of the outside diathe tube.
meters was carried out zs a simple micrometer
Measurements were made to three
measurement.
places, bat, owing to irregularity of the diameter of glass tubing, the third place is of
doubtful value.
Straight tips, horizontal tips with
a ninety degree bend near the end and vertical
tips with a bend of one hundred and eighty degrees were used but only the straight tips gave
The horizontal tips
satisfactory results.
gave very closely controlled velocities of flow,
but, owing to the fact that water entered the
lower part of the tip and cut down its effective
For differdiameter such tips were not used.
ent rates of flow the effective tip diameters
of such tips would be different, as they also
would for different depths of meter liquid.
Tips bent through one hundred and eighty degrees
are very unsatisfactory as the meter liquid enters
the tube and thus constantly varies the liquid
head in the meter.
The result of the variations
of liquid head is that the bubbles flow in a pulsating manner, which not only destroys the conditions of equilibrium, but also makes it impossible
to count the bubbles.
A tip cut with a hot wire was used and
proved unsatisfactory as the tube end was not
perfectly flat and at every projection a secondary stream of bubbles formed.
Tips that, after
having the projections ground or filed off, were
smoothed in the Bunsen flame and tips that were
ground on a fine abrasive wheel or oil stone did
not give any such troubles as did the plain cut
Attention should be called to the method
tip.
used by Harkins 2 for grinding dropping tips.
This method consists of filling the tip and also
surrounding it with "Wood's metal" and after
grinding tip, metal and all of removing the metal
by dipping the tip in hot water.
To determine the effect of changing the
liquid head on the operation of the meter, two
runs were made, in one of which the liquid depth
was one inch and in the other of which it was six
and one quarter inches.- The results of these
two runs are plotted, see Plate 8, and seem to
show that the volume number relation is not
appreciably changed by a slight change in the
The effect of a
height of the meter liquid.
change in liquid head can, however, be put to a
good use, as by changing the depth of the tip
without changing the setting of screw clamp "H"
the rate of flow is varied and thus control of
the meter can be obtained.
12
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The effect of impurities was studied
by adding a known weight of "Ivory" soap to the
meter liquid and making runs to obtain the data
necessary for plotting the curve.
The concentration of the soap solution was changed several
time- and runs were made for each soap concentration.
Too fewoooints were obtained to enable
the curve for the original soap concentration
to be plotted.
The results of the other runs
are plotted on plate 7 and show that for concentrated soap solutions the ratio of number to
volume is increased.
As the concentrations are
diminished the curve falls nearer and nearer that
When the
obtained with water in the meter.
concentration of soap is such that it can be seen
care, there
if the water is examined with a little
is no appreciable change in the number volume
ratio.
By adding a small amount of oil tp the
final soap concentration, 0.003 gms. per liter,
and emulsifying the oil, data was obtained for
This curve appears to show
curve(M) on Plate 8.
that an oil emulsion either has a higher surface
tension than water, or else the emulsion has a
Of the two possibilities
density less than onet
that of lowered density is undoubtedly the factor
responsible for the lowering of number volume
ratio.
As most impurities lower the surface
tension of water, their effect can be predicted
to be the same as that produced by dissolving
soap in the water.
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Plate q
19
The effect of different liquids in the
meter was determined by making runs on water, on
sulphuric acid , specific gravity 1.435, andOn
sulphuric acid, specific gravity 1.295.
The
runs made on these liquids are plotted on Plates
9,. 10 and 11.
Plate 10 shows a sharp change in
slppe in curve (M) beyond which point the points
vary wildly.
,Plate 11 shows the specific gravity
of the acid plotted against the volume of air
flowing when one hundred and twenty five bubbles
per minute pass through the meter.
No definite
conclusions can be drawn from this plot due to
its irregularity but possibly the irregularities
can be ex.)lained by the fact that increased
density and lessened surface tension in the
sulphuric acid tend to act so as to effect the
number volume ratio in different ways.
All runs were made by opening pinch
cock "I" and allowing air to flow through the
The
meter for one and sometimes two minutes.
bubbles were counted on a tallying counter and
In
the difference in graduate readings noted.
counting, attention should be focused on one
point in the meter, in the runs made such a point
Preliminary to making
was the end of the tube.
any runs the screw clamp "H" was opened wide
and air allowed to bubble rapidly through the
meter to saturate the meter liquid.
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24
Future
Work.
The inability to accurately measure volumes
greater than two hundred cubic centimeters by
means of apparatus similar to that used in this
investigation seems to necessitate the improvement of such apparatus.
To the end of so improveing the meter I would recommend that future investigators determine the extent to which an
aspirator bottle,with a horizontal tip and a
carefully maintained constant liquid head,could
Also in order that
be used as a bubble meter.
a bubble meter be capable of more universal use
I would also recommend that its possibilities
for the measurement of a heavy gas such as chlorine
be determined.
Conclusions
The use of a bubble-meter, as herein
described, is possible if volumes of less than
200 cubic centimeters per minute are to be
Several precautions must however be
measured.
taken; the tips must be smooth and approximately
horizontal, the liquids must be saturated with
the gas being measuredand rubber and not cork
stoppers should be used in the metering bottle.
The depth of the exit tip should not be more
than six nor less than one inch below the liquid
A bubble-meter should not be used to
surface.
measure gases other air or cases of nearly the
same weight, as Nitrogen or Oxygen,until further
A high
investigation has been carried out.
degree of accuracy can be expected if two or
The highest
more runs can be made to check.
percentage error obtained from Plate 2 is 20%
The
but the average is slightly less than 5%.
error of 20Z occurred at a velocity of 5 0.0.
per minute and for such a small displacement
the volume displaced cannot be measured closer
Larger
than 20% with the apparatus used.
tubes cannot be effectively used in a bubblemeter as the volume-number plot would have
too steep a slope to give any great accuracy.
APPENDIX
DATA
SHEET
tip number 1 1. dia. 0.167",
2
"
"
3
"f
"
4
"
"
0. dia. 0.1253"
0.1226".
0.320",
0. 367",
"
0(397"
0.410"
0. 456"
Meter liquid is water unless otherwise stated.
All volumes are in cubic centimeters.
Tip no.
Volume
4
5
3.(5
11
13
13
12
14
13
number
24. 5
26
20
60
65
65
63
80
65
1
volume number
16
80
15
80
22.. i5 104
101
21. f5
21. 5
108
20
105
109"
21
21
110
82
16
Tip no.
volume
14
13
14
15
13
15
25,
25
29
number
74
72
76
75
72
81
132
131
150
2
Volume
number
volume
number
volume
number
25
325
29
26
29
30
53
30
53
57
60
8
84
80
80
74
73
84
142
90
143
138
143
142
60
80
63
63
65
65
64
65
58
71
76
88
153
148
159
152
162
159
168
174
150
160
168
20 4
85
95
98
'10 5
105
1100
108
108
110
115
119
129
198
210
216
219
238
205
237
229
234
229
230
247
Tip no.
Volume
number
143
145
19
249
:245
44
volume
2
number
volume
number
Tip no. 3
volume
12
12
24
24
31
33
41
41
42
13
10
8
number
volume
number
volume
number
22
21
44
46
61
61
75
75
17
10
59
63
69
72
70
70
77
78
115
115
27
27
99
105
113
117
118
124
128
131
165
175
120
123
1:28
126
125
125
237
235
166
175
179
183
192
187
240
246
29
17
13
Tip no-. 4
volume number
23
32
35
48
53
53
54
54
53
55
41
49
51
78
83
83
75
75.
84
88
va-lumes
number
volume
number
56
56
55
58
58
63
60
60
70
80.
74
77
73
76
83
95
80
75
103
118
120
125
127
125
130
159
160
158
159
164
164
164
175
173
180
135
140
145
150
+
Tip no. 4
Volume
number
volume
number
150
160
175
185
190
195
205
225
230
230
230
135
190
195
230
245
245
250
250
285
285
285
290
297
295
300
226
234
236
241
241
245
280
242
254
257
Tip no.
494
202
216
214
211
223
230
222
227
216
4 is
45
101
102
165
170
235
50
50
30
30
number
67
135
140
198
204
225
75
67
39
40
254
252
the following runs unless
otherwise stated.
soap solution 0.,374 gms / liter.
used in
meter liquid is
Volume
21
25
55
volume
number
42
volume
50
55
number
82?
84
volume
150
143
nymber
201
199
82
meter liquid is
soap solution 0.094 gms //liter.
Volume
number
volume
number
volume
140
174
163
163
35
196,
209
207
193
46
35
120
150
140
95
48
180
186
178
123
90
45
45
30
35
number.
121
70
63
42
50
2q
Meter liquid is
Volume
170
180
65
65
number
214
216
volume
94
95
35
Volume
number
35
35
53
56
51
number
volume
25
25
35
Meter liquid is
35
soap solution 0.023 gms. / liter.
65
58
soap solution 0.011 gms.
volume
80
80
130
number
number
116
114
168
/ liter.
volume
number.
133
171
Meter liquid is soap solution 0.006 gms / liter.
Volume
170
175
178
170
number
volume
200
190
210
193
33
96
95
11
Meter liquid is
Volume
number
80
75
98
97
78
109
74
80
40
47
101
119
number
1'19
127
125
147
volume
volume
47
S22
62
114
123
1 17
115
62
165
number
70
227
148
158
151
151
210
145
33
11?
60
60
soap solution 0.003 gms.
82
/ liter.
volume
165
1590
170
220
215
number
number.
195
136
202
227
213
30
Meter liquid is
Volume
220
210
120
125
160
140
number
212
212
140
147
191
173
soap solution and oil.
volume
155
190
155
140
155
75
Meter liquid is water,
number
volume
number
181
241
174
164
192
102
75
100
100
105
50
50
104
134
129
134
72
75
depth is
6.25".
Volume
number
volume
number
volume
number
75
70
70
30
35
35
30
105
10 1
103
51
54
51
51
63
67
70
75
40
25
25
103
102
10 6
110
54
44
20
135
140
140
150
150
34
180
186
182
197
195
volume
number
Depth is
Volume
75
80
78
32
number
112
114
114
47
vp~lume
number
30
100
155
30
46
138
195
46
1.0".
160
160
194
196
Meter liquid is sulphuric acid unless otherwise stated
specific gravity is 1.435
Tip no.- 4
volume number
Volume number
volume number
249
199
193
135
95
95
90
95
165
170
180
214
237
226
189
138
137
136
137
220
230
244
185
170
205
190
200
270
285
177
175
45
43
Tip no.
Volume
150
175
180
185
170
220
220
220
85
90
90
number
236
228
234
238
227
243
249
245
120
175
179
volume
100
90
140
130
145
145
150
75
75
75
115
246
236
230
228
226
224
237
236
235
65
64
25
25
19
20
29
27
71
70
35
36
46
47
108
112
62
62
volume
number
43
40
37
87
3
number
196
182
226
207
228
:232
231
156
151
152
211
135
140
60
65
60
60
31
30
12
12
2525
233
129
136
134
132
72
71
32
32
Tip no. 9
Volume
number
volume
number
volume
number
27
23
85
40
36
29
102
103
4
24
90
40
133
233
140
50
156
5.15
6
23.,5
21.15
22
84
Volume
number
34
34
9.(5
24
211
211
75
151
9
10
32
62
64
40
113
183
189
Tip no. i
volume number
24
24
28
26
143
180
170
170
volume
number
14
15
110
111
.7
55
54
specific gravity of sulphuria acid 1.1295
Volume
number
volume
number
volume
36
39
12
13
13
45
50
48
222
225
228
19
20
18
117
115
113
51
232
49
17
17
232
116
38
38
38
41
138
196
215
205
111
6
5S. 5
number
190
210
85
89
39
39
37..'5
Tip no.
Volume
5.15
5.15
10
number
22
21.5
43
9. 15
37.15
9
37.15
volume
16
15
17
16
36
number
60
61
62
60
128
Tip no.
Volume
190
195
120
120
60
50
number
2383
242
190
192
106
102
volume
53
2
34
64
73
126
131
number
126
205
214
285
260
3
number
100
82
153
90
90
41
156
153
85
36
42
volume
volume
43
1.7.5
15
15
number
38
40
35.15
32.i5
11.5
27. 5
12.15
27.15
volume
number
110o
190
97
97
190
115
135
231
223
Tip no. 4
Volume
15
16. (5
29.65
number
30.15
34.15
33
59
64
63
Its
97
34.15
Sulphuric aci d sp.
volume
52
55
90
110
105
number
141
162
159
gr. 1.190
Volume 75
Number 126
Sulphuric acid sp. gr.- 1.089
Volume 88
Number 124
135
178
195
194
34
Bibliography
(1) 1919
A.F.Benton.
Rates of Flow.
(2)
1919
pp.
Gas Flow Meters for Small
623 -
Harkins and Brown.
J.
I.
E. Chem.
11.
Determination of
Surface Tension and the Weight of Falling Drops.
J. A. C. S.
41, pp. 499 / 524.